Problem: You are given N items.
The value of the i-th item (1 \leq i \leq N) is v_i.
Your have to select at least A and at most B of these items.
Under this condition, find the maximum possible arithmetic mean of the values of selected items.
Additionally, find the number of ways to select items so that the mean of the values of selected items is maximized.

Constraints

* 1 \leq N \leq 50
* 1 \leq A,B \leq N
* 1 \leq v_i \leq 10^{15}
* Each v_i is an integer.

Input

The input is given from Standard Input in the following format:


N A B
v_1
v_2
...
v_N


Output

Print two lines.
The first line should contain the maximum possible arithmetic mean of the values of selected items. The output should be considered correct if the absolute or relative error is at most 10^{-6}.
The second line should contain the number of ways to select items so that the mean of the values of selected items is maximized.

Examples

Input

5 2 2
1 2 3 4 5


Output

4.500000
1


Input

4 2 3
10 20 10 10


Output

15.000000
3


Input

5 1 5
1000000000000000 999999999999999 999999999999998 999999999999997 999999999999996


Output

1000000000000000.000000
1

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.math.*;
import java.awt.Point;
 
public class Main {
	//static final long MOD = 998244353L;
	//static final long INF = 1000000000000000007L;
	static final long MOD = 1000000007L;
	static final int INF = 1000000007;
	
	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		PrintWriter pw = new PrintWriter(System.out);
		
		int N = sc.ni();
		int A = sc.ni();
		int B = sc.ni();
		long[] nums = new long[N];
		HashMap<Long,Integer> hm = new HashMap<Long,Integer>();
		for (int i = 0; i < N; i++) {
			nums[i] = sc.nl();
			hm.put(nums[i],hm.getOrDefault(nums[i],0)+1);
		}
		Arrays.sort(nums);
		
		long val = nums[N-A];
		boolean allEqual = true;
		for (int i = N-1; i >= N-A; i--) {
			if (nums[i] != val) {
				allEqual = false;
			}
		}
		
		if (allEqual) {
			pw.println(val);
			int tot = 0;
			for (int i = 0; i <= N-A; i++) {
				if (nums[i] == val) {
					tot = N-i;
					break;
				}
			}
			long ans = 0;
			for (int i = N-A; i >= N-B; i--) {
				if (nums[i]==val) {
					ans += choose(tot,N-i);
				} else {
					break;
				}
			}
			pw.println(ans);
		} else {
			int used = 0;
			long sum = 0;
			for (int i = N-A; i <= N-1; i++) {
				if (nums[i] == val)
					used++;
				sum += nums[i];
			}
			pw.println((sum+0.0)/A);
			pw.println(choose(hm.get(val),used));
		}
		
		pw.close();
	}
	
	public static long choose(int n, int k) {
		int[] primes = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47};
		HashMap<Integer,Integer> hm = new HashMap<Integer,Integer>();
		for (int p: primes)
			hm.put(p,0);
		for (int i = 2; i <= n; i++) {
			int num = i;
			for (int p: primes) {
				int pow = 0;
				while (num % p == 0) {
					num /= p;
					pow++;
				}
				hm.put(p,hm.get(p)+pow);
			}
		}
		for (int i = 2; i <= k; i++) {
			int num = i;
			for (int p: primes) {
				int pow = 0;
				while (num % p == 0) {
					num /= p;
					pow++;
				}
				hm.put(p,hm.get(p)-pow);
			}
		}
		for (int i = 2; i <= (n-k); i++) {
			int num = i;
			for (int p: primes) {
				int pow = 0;
				while (num % p == 0) {
					num /= p;
					pow++;
				}
				hm.put(p,hm.get(p)-pow);
			}
		}
		long ans = 1;
		for (int p: hm.keySet())
			ans *= ((long)Math.pow(p,hm.get(p)));
		return ans;
	}
 
	public static long dist(long[] p1, long[] p2) {
		return (Math.abs(p2[0]-p1[0])+Math.abs(p2[1]-p1[1]));
	}
	
	//Find the GCD of two numbers
	public static long gcd(long a, long b) {
		if (a < b) return gcd(b,a);
		if (b == 0)
			return a;
		else
			return gcd(b,a%b);
	}
	
	//Fast exponentiation (x^y mod m)
	public static long power(long x, long y, long m) { 
		if (y < 0) return 0L;
		long ans = 1;
		x %= m;
		while (y > 0) { 
			if(y % 2 == 1) 
				ans = (ans * x) % m; 
			y /= 2;  
			x = (x * x) % m;
		} 
		return ans; 
	}
	
	public static int[] shuffle(int[] array) {
		Random rgen = new Random();
		for (int i = 0; i < array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    int temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
		return array;
	}
	
	public static long[] shuffle(long[] array) {
		Random rgen = new Random();
		for (int i = 0; i < array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    long temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
		return array;
	}
	
	public static int[][] shuffle(int[][] array) {
		Random rgen = new Random();
		for (int i = 0; i < array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    int[] temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
		return array;
	}
	
    public static int[][] sort(int[][] array) {
    	//Sort an array (immune to quicksort TLE)
 
		Arrays.sort(array, new Comparator<int[]>() {
			  @Override
        	  public int compare(int[] a, int[] b) {
				  return a[0]-b[0]; //ascending order
	          }
		});
		return array;
	}
    
    public static long[][] sort(long[][] array) {
    	//Sort an array (immune to quicksort TLE)
		Random rgen = new Random();
		for (int i = 0; i < array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    long[] temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
		Arrays.sort(array, new Comparator<long[]>() {
			  @Override
        	  public int compare(long[] a, long[] b) {
				  if (a[0] < b[0])
					  return -1;
				  else if (a[0] > b[0])
					  return 1;
				  else
					  return 0;
	          }
		});
		return array;
	}
    
    static class FastScanner { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastScanner() { 
            br = new BufferedReader(new InputStreamReader(System.in)); 
        } 
  
        String next() { 
            while (st == null || !st.hasMoreElements()) { 
                try { 
                    st = new StringTokenizer(br.readLine());
                } catch (IOException  e) { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        }
        
        int ni() { 
            return Integer.parseInt(next()); 
        }
  
        long nl() { 
            return Long.parseLong(next()); 
        } 
  
        double nd() { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() {
            String str = ""; 
            try { 
                str = br.readLine(); 
            } catch (IOException e) {
                e.printStackTrace(); 
            } 
            return str;
        }
    }
}